{
  "id": "1804.04501",
  "version": "v1",
  "published": "2018-04-10T18:26:17.000Z",
  "updated": "2018-04-10T18:26:17.000Z",
  "title": "Representation of Hamilton-Jacobi equation in optimal control theory with compact control set",
  "authors": [
    "Arkadiusz Misztela"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1507.01424",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper we study the existence of sufficiently regular representation of Hamilton-Jacobi equation in optimal control theory with the compact control set. We introduce a new method to construct a representation for a wide class of Hamiltonians, wider than it was achieved before. Our result is proved by means of these conditions on Hamiltonian that are necessary for the existence of a representation. In particular, we solve an open problem of Rampazzo (2005). We apply the obtained results to reduce a variational problem to an optimal control problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-10T18:26:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26E25",
      "49L25",
      "34A60",
      "46N10"
    ],
    "keywords": [
      "optimal control theory",
      "compact control set",
      "hamilton-jacobi equation",
      "optimal control problem",
      "sufficiently regular representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}